Spirit's Airbus 319 jetliner took off from Detroit Metropolitan Airport bound for Dallas on Sunday evening.
Officials say the Spirit pilot was told there was a skydiving plane nearby as he took off, which the pilot also observed.
Suddenly, an alarm sounded in the cockpit, telling the pilot to nosedive from nearly 2,000 feet. At the closest, the two planes were 1.6 miles apart horizontally and 400 feet vertically, FAA spokeswoman Elizabeth Cory said.
Passengers say it was horrifying.
"We were lifted from our seats. The entire cabin was screaming and crying," said passenger Janet Dunnabeck.
Spirit says no passengers were injured, its pilots followed appropriate procedures and the flight continued without incident.
Addressing why the two planes got dangerously close, the FAA pointed to the smaller plane's pilot.
"The skydiving plane was flying under Visual Flight Rules, under which pilots are responsible for seeing and avoiding other aircraft," Cory said.
The Associated Press contributed to this report.